where \(a_i\)  is the mean intra-cluster distance from sample \(i\) , and \(b_i\)  is the mean nearest-cluster distance from \(i\)  to each sample.
Note that a higher value is related to better-defined clusters.
The Calinski-Harabasz Index (CHI) [1]} is given by
\(\text{CHI} = \frac{\text{SS}_M}{\text{SS}_W} \frac{N-k}{k-1},\) 
